What Shall I Do Next?

I have been wondering whether or not I will stay in Korea. I know I need a vacation. My contract ends on June 30. I can stay in the country for 30 days without a valid visa. Well, most likely, I will be flying out on July 1. I haven't bought tickets yet. I do want to see some things before I fly out of here. I especially want to see Gyeongju, the ancient capital city. There are awesome tomb mounds and ruins to see. I also still haven't been to Cheju Island, the biggest island off the coast of Korea. It's a popular honeymoon spot for Koreans.